Method and system for decoding multilevel signals

ABSTRACT

A multilevel optical receiver can comprise a plurality of comparators that generally correspond with the number of levels in a multilevel data stream. Each comparator can be individually controlled and fed a decision threshold in order to decode a multilevel signal. The multilevel optical receiver can generate a statistical characterization of the received symbols in the form of a marginal cumulative distribution function (CDF) or probability density function (pdf). This characterization can be used to produce a set of ε-support estimates from which conditional pdfs are derived for each of the transmission symbols. These conditional pdfs may then be used to determine decision thresholds for decoding the received signal. The conditional pdfs may further be used to continuously estimate the fidelity or error rate of the received signal without the transmission of a testing sequence. The ε-supports may further be used to automatically control the gain on the receiver.

CROSS REFERENCE TO RELATED APPLICATIONS

The present application claims priority under 35 U.S.C. § 119(e) to U.S.Provisional Application Ser. No. 60/281,526 entitled, “AutomaticThreshold Tracking and Digitization Method for Multilevel Signals,”filed on Apr. 4, 2001 in the name of Hietala et al. The entire contentsof which are hereby incorporated by reference. This application is alsorelated to U.S. Non-provisional application Ser. No. 10/032,586entitled, “Increasing Data Throughput in Optical Fiber TransmissionSystems,” filed on Dec. 21, 2001.

FIELD OF THE INVENTION

The present invention relates to optical fiber communication systems andincreasing the throughput of data transmission over an optical fibercommunication system through the use of multilevel modulation.Specifically, the present invention relates to a method and system fordemodulating multilevel signals.

BACKGROUND OF THE INVENTION

The use of multilevel signals in an optical network architectureincreases channel data throughput rates without requiring replacement ofthe existing optical fiber in a link (i.e., the optical fiber plant).While multilevel signals can offer this advantage of increased channeldata throughput rates to an optical network architecture, conventionalhardware and software used to decode the multilevel signal often cannotachieve this advantage because of difficulties in establishingthresholds by receivers for a multilevel signal. These thresholds areneeded by the receiver to decode the multilevel signal into the one ormore symbols that make up the multilevel signal.

The difficulties in establishing the thresholds are associated withreliably characterizing the noise that is present within a multilevelsignal. Further, conventional hardware and software do not addressmultilevel signals comprising greater than two-level data streams. Thatis, the conventional art only provides methods for automaticallycontrolling the threshold or decision points for traditional two-leveldata streams.

The voltage detection thresholds or decision points of multilevelreceivers are usually centered in a statistical center of each of thetroughs of a graphical representation of a marginal probability densityfunction (pdf) that corresponds to the “eyes” of an “eye diagram” for amultilevel signal in order to minimize the number of decoding errors.Since the troughs or “eyes” of a pdf are usually not uniformlydistributed in voltage, a simple conventional direct analog-to-digitalconversion (ADC) at a minimum number of bits is not adequate fordecoding a multilevel signal.

Conventional receivers for decoding two-level multilevel signalsfrequently assume additive noise with parametric noise distributionssuch as a Gaussian distribution. Conventional receivers for decodingtwo-level multilevel signals also usually assume simple lineardependencies on the transmitted two-level multilevel signal.

However, the noise in optical channels of a multilevel signal may havedistributions that are non-Gaussian. Further, the distortion ofmultilevel signals may be nonlinear in nature resulting in asymmetric ormulti-modal pdfs for the received signal.

In addition to the problems associated with estimating noisedistributions in a multilevel signal, another problem exists in theconventional art with respect to reliably determining the fidelity of areceived multilevel signal without the explicit transmission of a“testing” data sequence that is already known to the receiver.Conventional performance monitors can generally be categorized into oneof two sets.

The first set are those that use a secondary threshold (or samplingphase) to approximately determine how often a received symbol is near tothe primary threshold (or sampling phase) used for decoding. When thedetected sample from this second threshold differs from the primarysample, a pseudo-error is said to have occurred. The link is thencharacterized with the pseudo-error rate. This class of approaches,however, neglects the fact that under optimal filtering, the primary andsecondary samples will be heavily statistically correlated, and thus,misrepresents the link performance.

The second set of performance monitors of the conventional art are thosethat rely on acquiring statistics from an error correction module.Specifically, forward error correction coding is used at the transmitterto allow the receiver to correct a small number of errors. If the truenumber of errors incurred during transmission is sufficiently small,then the receiver can correct all of the errors and report the rate atwhich errors occur. This class of performance monitors, however, sufferstwo significant drawbacks.

First, these methods require the use of an error correction code so thaterrors can be detected. The second drawback is that transmission errorsmust occur in order to acquire statistics regarding their frequency ofoccurrence. By the very nature of the high quality of the link, theseerrors will rarely occur, and thus, the performance monitor requires asignificant amount of time to reliably report the error rate.

In view of the foregoing, there exists a need in the art for amultilevel signal receiver that does not assume a particular noisedistribution in a received multilevel signal. That is, a need exists inthe art for a multilevel signal receiver that employs robust estimatesof noise distributions in order to process complex signal distortionsthat may be present in a multilevel signal while maintaining highperformance for classic Gaussian noise distributions that may also bepresent in a multilevel signal. Aspects include the need in the art for(1) a method and system for automatically selecting the decisionthresholds for a multilevel signal receiver on an adaptive basis, (2) amultilevel signal receiver that can process multi-modal conditionalprobability density functions, and (3) a method and system for decodingmultilevel signals that can provide a reliable fidelity measure of thereceived signal without the transmission of explicit error testingsequences known to the receiver. In other words, a need exists in theart for a complete statistical characterization of link noise toreliably establish decision thresholds and infer error rates withoutsuffering from the aforementioned drawbacks of the conventional art.

SUMMARY OF THE INVENTION

The present invention solves the aforementioned problems by providing asystem and method for decoding multilevel signals. More specifically,the present invention is generally drawn to a method and system forselecting an optimal set of decision thresholds that can be used by anoptical receiver in order to decode a multilevel optical signal. In oneexemplary embodiment, the multilevel optical receiver can comprise aplurality of comparators that generally correspond with the number oflevels in a multilevel data stream. Each comparator can be individuallycontrolled and fed a decision threshold in order to decode a particularchannel from a multilevel signal.

Unlike conventional optical receivers, the present invention canautomatically control the thresholds or decision points for comparatorsof multilevel optical receivers that process multilevel data streams,where the noise corrupting the received signal is not necessarilyGaussian, signal independent, nor time-invariant. In other words,multilevel data streams can be distorted by noise where the noisefollows a non-Gaussian probability distribution whose parameters dependon the transmitted signal values and vary with time. However, thepresent invention can still effectively process multilevel signals thathave Gaussian, time-invariance, or signal-independence characteristics.

According to one aspect of the present invention, a multilevel opticalreceiver can comprise a plurality of voltage comparators, a decoder, alatch, an analog low-pass filter coupled to the latch, and a low-speedhigh resolution analog-to-digital converter coupled to the low-passfilter. With such structure, the multilevel optical receiver cangenerate an estimate of a cumulative distribution function (CDF) basedon the received multilevel data signal.

The CDF can completely characterize the received multilevel data signal.

From the CDF, the optical receiver can further generate an equivalentmarginal probability density function (pdf) which is used to determine anear-optimal set of decision thresholds. A marginal pdf can be definedas an “overall” pdf characterizing the received signal when randomsymbols are transmitted. A marginal pdf can comprise one or moreconditional pdfs. A conditional pdf is the pdf for an individual symbolof a multilevel signal, i.e. the pdf of the received signal conditionedon a particular symbol being transmitted.

Instead of using the calculated pdf to determine an optimal set ofthresholds, the CDF function itself in one exemplary embodiment can beused to determine the decision thresholds as it conveys the sameinformation as the pdf but in a less intuitive form. In either case, theinvention can assist with centering the voltage detection thresholds foreach of the plurality of comparators. In the pdf exemplary embodiment,the invention can center the voltage detection thresholds at the troughsor local minima of the pdf (or equivalently at the points of inflectionof the CDF) which correspond to near-optimal decision thresholds for thereceived signal. In this way, the probability of error in the detectionof the individual symbols that make-up multilevel signal can beminimized.

The centering of voltage detection thresholds based upon the calculatedpdfs can involve several different steps. In one exemplary embodiment, afirst step can comprise calculating an initial set of ε-supportestimates corresponding to ranges of received voltages of significantprobability for receiving a particular symbol. Next, the ε-supportregions are combined until there is a 1-to-1 correspondence between thetransmitted symbol levels and the ε-support regions. Possible thresholdcandidates can then be determined by establishing the threshold betweenthe ε-support regions.

According to another aspect of the present invention, a multileveloptical receiver can comprise a plurality of voltage comparators, ananalog low-pass filter, and a low-speed high resolutionanalog-to-digital converter coupled to the low-pass filter. According tothis exemplary aspect, a latch that can be coupled to the low-passfilter has been removed. The removal of this latch can change the regionof the signal that is being characterized. Specifically, latching thecomparator output focuses the CDF/pdf characterization to the portion ofthe signal synchronized with the system clock and decision output. Byremoving the latch, the statistical characterization applies to theentire received signal and not just that portion which is used for thedecision output.

For an alternative exemplary embodiment of the present invention, theCDF and pdf can be generated in a digital fashion (rather than theanalog fashion described above) by using a track-and-hold circuit or asample-and-hold circuit. The track-and-hold circuit or thesample-and-hold circuit can sample an input multilevel data signal andaccumulate the samples over time. These samples can then be digitallyprocessed to provide either a marginal pdf or CDF. As before, the CDF orpdf may then be used to determine the decision threshold voltages.

According to another alternative exemplary embodiment of the presentinvention, a high-resolution analog-to-digital converter (ADC) canmeasure the voltage of the received multilevel signal. The digitizedmultilevel signal can be provided to a digital signal processor (DSP)which computes the pdf and decision thresholds. The DSP can then use thecomputed thresholds to decode subsequent symbols digitized from themultilevel signal.

Those skilled in the art will recognize that different hardware orsoftware or both can be substituted for the exemplary embodimentsdescribed herein without departing from the scope and spirit of thepresent invention. Specifically, as long as the hardware or software (orboth) performs the functions described herein, then those skilled in theart will appreciate that the present invention would be embodied in suchalternative hardware or software or both.

A further aspect of the invention can include calculating the fidelityof a multilevel signal based upon an estimated marginal pdf.Specifically, the marginal pdf can be used to estimate a set ofconditional pdfs (one for each candidate symbol of a multilevel signal).These conditional pdfs can then be used to estimate the probability oferror for each symbol and hence the system as a whole. This aspect ofthe invention allows for error performance to be measured withoutexplicit error tests that require testing sequences (known to thereceiver) to be transmitted.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a bock diagram of a fiber optic link constructed in accordancewith an exemplary multilevel optical signal system.

FIG. 2 is a block diagram of an exemplary multilevel optical receiveraccording to an exemplary embodiment of the present invention.

FIG. 3A is a diagram showing a representative example of an ideal16-level signal.

FIG. 3B is an exemplary simulated received signal displaying the signalin FIG. 3A transmitted through 80 km of optical fiber.

FIG. 3C illustrates an exemplary Eye-diagram for 4,096 simulated symbolsreceived through 80 km of optical fiber.

FIG. 4 illustrates a block diagram of an exemplary embodiment for a16-level multilevel optical receiver.

FIG. 5A illustrates a block diagram of another exemplary embodiment fora 16-level multilevel optical receiver.

FIG. 5B illustrates a block diagram of yet another exemplary embodimentfor a 16-level multilevel optical receiver.

FIG. 5C illustrates a block diagram of yet a further exemplaryembodiment for a 16-level multilevel optical receiver.

FIG. 6A illustrates an exemplary cumulative distribution function (CDF)for the received signal of FIG. 3C sampled at the horizontal eye-center.

FIG. 6B illustrates an exemplary marginal probability density function(pdf) for the received signal of FIG. 3C sampled at the horizontaleye-center.

FIG. 7 illustrates a block diagram of alternative exemplary embodimentfor a 16-level multilevel optical receiver.

FIG. 8A illustrates another exemplary eye diagram for simulated data ofa 16-level transmission.

FIG. 8B illustrates a histogram of the data shown in FIG. 8A.

FIG. 9 is an exemplary logic flow diagram illustrating a method fordecoding a multilevel signal.

FIG. 10 is an exemplary logic flow diagram illustrating a sub-method ofFIG. 9 for calculating a cumulative distribution function according toan exemplary embodiment of the present invention.

FIG. 11 is an exemplary logic flow diagram illustrating a sub-method ofFIG. 9 for calculating a marginal probability density function accordingto an exemplary embodiment of the present invention.

FIG. 12 is an exemplary logic flow diagram illustrating a sub-method ofFIG. 9 for calculating a marginal probability density function accordingto alternate exemplary embodiment of the present invention.

FIG. 13 is an exemplary logic flow diagram illustrating a sub-method ofFIG. 9 for calculating one or more decision thresholds according to anexemplary embodiment of the present invention.

FIG. 14 is an exemplary logic flow diagram illustrating a sub-method ofFIG. 9 for calculating the fidelity of a multilevel signal according toan exemplary embodiment of the present invention.

FIG. 15 illustrates a graph of an exemplary measured pdf for an N=16level multilevel signal according to an exemplary embodiment of thepresent invention.

FIG. 6 illustrates a graph of an exemplary initial pdf estimate for anN=16 level multilevel signal according to an exemplary embodiment of thepresent invention.

FIG. 17 illustrates a graph of an exemplary revised pdf estimate for anN=16 level multilevel signal according to an exemplary embodiment of thepresent invention.

FIG. 18 illustrates a graph of the log-likelihood ratio of an exemplaryinitial pdf estimate over the measured pdf for an N=16 level multilevelsignal according to an exemplary embodiment of the present invention.

FIG. 19 illustrates a graph of the log-likelihood ratio of an exemplaryrevised pdf estimate over the measured pdf for an N=16 level multilevelsignal according to an exemplary embodiment of the present invention.

FIG. 20 illustrates a graph with a measured pdf along with decisionthresholds and fidelity characterizations for an N=16 level multilevelsignal according to an exemplary embodiment of the present invention.

DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS

The present invention can select a near-optimal set of decisionthresholds that can be used by an optical receiver in order to decode amultilevel optical signal. The multilevel optical receiver can comprisea plurality of comparators that generally correspond with the number oflevels in a multilevel data stream. Each comparator can be individuallycontrolled and fed a decision threshold in order to decode a particularsymbol from a multilevel signal. Alternatively, a high-resolutionanalog-to-digital converter (ADC) can measure the voltage of thereceived multilevel signal. The digitized multilevel signal can beprovided to a digital signal processor (DSP) which computes the pdf anddecision thresholds. The DSP can then use the computed thresholds todecode subsequent digitized symbols from the multilevel signal.

The present invention typically does not require the assumption ofGaussianity, time-invariance, signal-independence, or binary signaling.Contrary to the conventional art, the invention is designed to performwell when these assumptions do not hold. However, the present inventioncan also perform well if the assumptions do hold or are valid.

A CDF can completely characterize the received multilevel signal data.From the CDF, the optical receiver can further generate an equivalentmarginal probability density function (pdf) which is used to determinean optimal set of decision thresholds. A marginal pdf can be defined asan “overall” pdf characterizing the received signal when the symboltransmitted is unknown. A marginal pdf can comprise one or moreconditional pdfs. A conditional pdf is the pdf for an individual symbolof a multilevel signal, i.e. the pdf of the received signal conditionedon a particular symbol being transmitted.

The determining of voltage detection thresholds based upon thecalculated pdfs can involve several different steps. In one exemplaryembodiment, a first step can comprise calculating an initial set ofε-support estimates that comprise ranges of received voltages. Next, theε-support regions are combined until there is a 1-to-1 correspondencebetween the transmitted symbol levels and the ε-support regions.Possible threshold candidates can then be determined by establishing thethreshold between the ε-support regions.

Referring now to the drawings, in which like numerals represent likeelements throughout the several Figures, aspects of the presentinvention and the illustrative operating environment will be described.

FIG. 1 is a functional block diagram illustrating an exemplary opticalnetwork architecture 100 according to the present invention. Theexemplary optical network architecture 100 comprises a transmitter 110that includes the circuitry necessary to modulate the light source 120with the incoming multiple channel digital data input stream. The lightsource 120 is usually a laser in the form of a laser diode or anexternally modulated laser source such as a Mach-Zehnder, orElectro-Absorptive modulator. The transmitter 110 takes a set of nhigh-speed digital binary inputs or channels and converts them to asingle multilevel digital signal comprising 2^(n) levels at the samesymbol rate (and thus an n times faster data rate) as the input datachannels.

The exemplary optical network architecture 100 further comprises anoptical waveguide 130 that can include one or more spans of opticalfiber. The optical waveguide 130 couples the light source 120 to anoptical detector 140. The optical detector 140 can be coupled to areceiver 150 that is responsible for decoding the multilevel signal intoone or more channels of digital data output. The receiver 150 takes asingle multilevel digital signal comprising 2^(n) levels at the samesymbol rate and converts the multilevel signal into a set of nhigh-speed digital binary inputs or channels. The receiver 150 typicallycomprises all circuitry required to operate a corresponding opticaldetector 140 and to amplify the detected signal. Further details of thereceiver 150 will be discussed below with respect to FIG. 2.

Referring now to FIG. 2, this figure illustrates a block diagram of anexemplary multilevel receiver 150 according to an exemplary embodimentof the present invention that can also be referred to as a desymbolizer.The receiver 150 can comprise an optical detector and TransImpedanceAmplifier (TIA) circuitry 140. Usually, the TransImpedance Amplifiertakes a very small electrical current output by the optical detector andconverts it to a proportional voltage with a moderate intensity(“moderate” in the sense that it may still need further amplification).As noted above, the optical detector 140 coverts an optical signal intoan electrical signal. The optical detector 140 is coupled to anamplifier 210 that feeds its output into a signal conditioning filter215. The gain of the amplifier 210 can be controlled by a signalintegrity unit (SIU) 220.

The optional signal conditioning filter 215 can comprise one or moreprogrammable analog signal processing modules such as equalizers andfilters. The signal conditioning filter 215 is also coupled to andcontrolled by the SIU 220. The SIU 220 can determine the decision orvoltage thresholds that are used to decode the multilevel signal.Further details of various exemplary embodiments of the SIU 220 will bediscussed below with respect to FIGS. 4, 5, and 7.

A clock recovery unit 225 can be coupled to the output of the amplifier210 or an optional signal conditional filter 215. The clock recoveryunit 225 can generate a timing signal that is used to operate anoptional holding circuit 230 and an analog-to-digital converter (ADC)235. The holding circuit 230 is not required for each of the exemplaryembodiments. The holding circuit 230 can comprise one of atrack-and-hold circuit or a sample-and-hold circuit as known to thoseskilled in the art. The holding circuit 230 is coupled to the output ofthe signal conditioning filter 215.

Coupled to the output of the optional holding circuit 230 is the ADC 235which decodes the multilevel signal. The ADC 235 can convert a2^(n)-level signal into n binary data streams. Further details ofvarious exemplary embodiments of the ADC 235 will be discussed belowwith respect to FIGS. 4, 5, and 7. The ADC 235 having a decoder 410 (notshown in FIG. 2) can convert a coded n-bit word each clock cycle intothe corresponding n-bit word that was initially input into thetransmitter 110. All of these functional blocks, less the opticaldetector and TIA circuitry 140 can be integrated into one circuit or ona multi-chip module.

Background on Multilevel Signals

FIG. 3A is a graph 300 depicting time versus voltage of an exemplarymultilevel amplitude shift keying (ASK) signal 305 that combines fourbits into a single transmitted pulse, or symbol, possessing one of 16possible amplitude levels. While the present invention contemplates ASKsignals, other modulation techniques are not beyond the scope of thepresent invention. Other modulation techniques include, but are notlimited to, frequency shift keying (FSK), phase shift keying (PSK),quadrature amplitude modulation (QAM), and other like modulationtechniques.

In FIG. 3A, five different amplitude values 310, 315, 320, 325, and 330are shown. Associated with each amplitude value can be a unique n=4 bitword. For example, the amplitudes 310, 315, 320, 325, and 330 could beassociated with the words “0010”, “0101”, “0111”, “0001”, and “0110”.Specifically, associated with the first amplitude value 310 can be thefour bit word of “0010.” Associated with the second amplitude value 315,which is higher in voltage than the first value 310, can be the four bitword of “0101.” Associated with the third amplitude value 320, which ishigher in voltage than the second value 315, can be the four bit word of“0111.” Associated with the fourth amplitude value 325, which is thelowest value out of all the values, can be the four bit word of “0001.”And lastly, associated with the fifth amplitude value 330, which isbetween the second and third values 315 and 320, can be the four bitword of “0110.” Those skilled in the art will appreciate that otherwords or assignments can be made for each amplitude value of amultilevel signal without departing from the scope and spirit of thepresent invention.

A multilevel signal allows for more than one bit to be transmitted perclock cycle, thereby improving the spectral efficiency of thetransmitted signal. For multilevel optical transmission, somecharacteristic (i.e., signal property) of a transmitted pulse (such asamplitude, phase, frequency, etc.) is modulated over 2^(n) levels inorder to encode n bits into the single pulse, thereby improving thespectral efficiency of the transmitted pulse. Multilevel modulation canincrease aggregate channel throughput by combining n OOK data streams(each with bit rate, B, in bits/s) into one 2^(n)-level signal (with asymbol rate, B, in symbols/s) for an aggregate throughput (in bits/s)that is n times greater than B. The aggregate data rate of the 16-levelsignal shown in FIG. 3 is four times greater than a corresponding OOKsignal with a bit rate equal to the multilevel symbol rate. As thesimplest case, OOK can be regarded as a two level multilevel signalwhere the symbol rate and bit rate are equal.

As a specific example, the assumption may be made that the 16-levelsignal in FIG. 3 has a symbol rate of 2.5 Gsym/s. That is, a pulse e.g.,with one of 16 possible amplitudes (e.g. 310, 315, 320, 325, and 330) istransmitted at a rate of 2.5 Gigapulses/s. Therefore, the aggregate datarate of the 16-level signal is actually 10 Gb/s (4×2.5 Gb/s) becauseeach pulse (i.e., symbol) can represent a distinct value of four bits.The optical components required to transmit and receive a 16-level 2.5Gsym/s signal are nearly identical to those required for transmittingand receiving an OOK 2.5 Gb/s signal.

Exemplary Portion of a Simulated Received Multilevel Signal

Referring now to FIG. 3B, this figure is a graph 350 of time versusvoltage depicting an exemplary simulated received 16-level multilevelsignal 355 that was propagated through 80 kilometers of optical fiber.The received 16-level multilevel signal 355 shown in FIG. 3B is anillustration of a segment covering eight symbols of the simulatedwaveform. The simulated waveform is based on 80 kilometers of fiber andan Avalanche PhotoDiode (APD). An APD can convert the optical signal toan electrical current whose amplitude is proportional to the receivedoptical power. The simulated received multilevel signal 355 illustratesthe challenge of directly determining the levels of each data streamcontained in the signal.

Exemplary Eye-diagram for Received Multilevel Signal

Referring now to FIG. 3C, this figure is a graph 360 of time versusvoltage depicting an exemplary “Eye”-diagram 365 for all 4,096 receivedsymbols corresponding to the transmitted signal 305 of FIG. 3A. Eyediagram 365 comprises the complete data set with all symbol periodsoverlaid on one another. An Eye diagram/Eye pattern comprises thereceived signal displayed on an oscilloscope to show how distinct thereceived levels are. Often, an “open” eye 370 shows a good qualitysignal with clear differences between levels. A “closed” eye means thatsome levels could be confused for other levels, and therefore is a signof a poor transmission system.

Eye diagram 365 illustrates the difficulty in determining the thresholdsfor multilevel data streams. From this simulation, it is apparent thatthe noise is signal dependent. Specifically, larger signal levelsusually have a larger associated noise variance as is evidenced by thethickening of the eye-lids towards the top of the eye-diagram 365. It isdesired to have voltage detection thresholds centered in the statisticalcenter of each of the 15 “eyes” 370. Furthermore, the eyes 370 are nolonger uniformly distributed in voltage because the transmitter (withprior knowledge of the signal dependent noise variance) spaces thetransmitted levels in a nonuniform manner in order to minimize thesusceptibility to the noise and hence minimize the probability of error.

Because the transmitted levels are not uniformly spaced, a simpleconventional direct ADC 235 at the minimum number of bits (log₂(16)=4 inthis case) is not adequate. Hypothetically, the received voltage signalcould be digitized at a higher resolution (additional bits) and signalprocessing applied to determine the correct level. Unfortunately, at thetargeted symbol rates of many optical systems (i.e. OC-192 at 10 Gb/s),this would require order-of-magnitude speed improvements of readilyavailable ADC and signal processing technologies.

Exemplary Embodiments for Analog-to-digital Converters (ADCs) and SignalIntegrity Units (SIUs)

Referring now to FIG. 4, this figure illustrates the details of anexemplary ADC 235 and a SIU 220. The ADC 235 may comprise a plurality offirst comparators 405 connected in parallel to a decoder 410. The ADC235 may be characterized as a high-speed low-resolution ADC thatconverts the received multilevel signal (symbols) into the associatedtransmitted data words or data channels. The threshold voltages of thecomparators 405 are controlled by one or more digital-to-analogconverters 415. The decoder 410 is coupled to an exemplary first latch420 that may be four bit latch type. A second comparator 425 isconnected in parallel with the first comparators 405. However, thesecond comparator 425 does not feed its output to the decoder 410.Instead, the output of the second comparator 425 is fed into a secondoptional latch 430 which is controlled by the clock signal. Thesubcircuit comprising the second comparator 425 and the optional latch430 is referred to as the event-detection circuit (EDC), as illustratedin FIG. 4, since it produces a binary signal indicating if a particularevent (in this case the event is whether v_(rv) exceeds v_(in) asdiscussed later) has occurred.

The comparator 425 used in the EDC should ideally be identical to and inthe same environment as the first comparators 405. This will allow forthe SIU to accurately determine threshold settings of the ADC with aone-to-one voltage correspondence. Assuming that the ADC 235 is in theform of an integrated circuit (IC), the first comparators 405 and thesecond comparator 425 should be realized with the same basic circuitryand located in the same region of the IC to provide good thermalmatching. In other words, the first comparators 405 and the secondcomparator 425 in this exemplary embodiment are manufactured on orwithin the same integrated circuit in order to improve thermal matching.

The output of the second optional latch 430 is fed into a filter 435that is part of the signal integrity unit 220. The output of the secondoptional latch 430 is called Event Detection (ED). After low-passfiltering by the LPF 435, the DC component remains and is termed theevent monitor voltage v_(em) and is an analog probability estimate forthe controlled reference voltage v_(rv) exceeding the received signalv_(in) where v_(rv) is generated by the digital-to-analog converters415. Further details of the analog probability estimate v_(em) and thecontrolled reference voltage v_(rv) will be discussed below.

The output of the second optional latch 430 can be fed to a secondanalog-to-digital converter 440 that is part of the signal integrityunit 220. Opposite to first ADC 235, the second ADC 440 may becharacterized as a low-speed high-resolution ADC that measures theaveraged event-detector output representing the CDF value. Specifically,the reference voltage v_(rv) is swept over a range of voltage levelswhile the second ADC 440 samples the voltage v_(em) from the filter 435to produce an estimate of the CDF.

More specifically, pseudo-code to construct the CDF could comprise oneor more of the following steps: Step 1: Set the reference voltage v_(rv)to the minimum value of interest, i.e. lowest possible received voltage.This could be referred to as the start of the sweep. Step 2: Measure theaveraged event-detector output voltage v_(em) and take that value as theCDF value for the set reference voltage. Step 3: Increment the referencevoltage. Step 4: If the reference voltage is above the maximum value ofinterest, a “sweep” has been completed and then the reference voltage isreset and the process returns to Step 1. Otherwise, the process of“sweeping” continues and returns to Step 2. It is noted that a singlepoint of the CDF (step 2) is obtained for each value of the referencevoltage.

Therefore, the SIU 220 sets v_(rv) to a fixed value and then measuresthe averaged ED output. The SIU 220 then sets v_(rv) to a differentfixed value and measures another point of the CDF. This process iscompleted until the CDF curve is formed.

The second ADC 440 feeds its output to a microcontroller 445.Microcontroller 445 processes the cumulative distribution function (CDF)to determine threshold voltage values for the first comparators 405.Further details of the microcontroller's processing of the CDF will bediscussed below with respect to FIGS. 6A, 6B, and 9. The microcontroller445 is responsible for feeding the threshold voltage values to the firstcomparators 405 for decoding the multilevel signal.

FIG. 4 illustrates a portion of a 16 level receiver 150, but it shouldbe obvious to one skilled in the art that this circuit can be readilyextended to any number of levels. For 16-levels (N=16) there isnecessarily 15 (or N−1) voltage decision levels.

Through the use of the second optional latch 430 in FIG. 4, the portionof the signal analyzed can be restricted to the eye-opening sampled onceeach clock period. In this case, the resulting estimated cumulativedistribution function (CDF) reports the distribution of received analogsignal values at the sampling point used in the decision circuitry inthe receiver 150, i.e. the signal timing used by the first comparators405 is the same as that used by the EDC. This synchronization preventsother regions of the signal from corrupting the estimation process.

Although the data rate of the received signal can be very high (e.g. onthe order of tens of gigabits per second), receiver 150 of the presentinvention does need not sample the signal at this high rate to analyzethe signal. The receiver 150 avoids this impediment by using the simplehigh-speed second comparator 425 that indicates whether a controlledreference voltage exceeds the received signal at the clocked sampletime. The resulting binary signal can then be averaged in time with theanalog low-pass filter 435 to estimate the probability that thereference voltage exceeds the received signal. This probability estimateis a slowly-varying (ideally a constant) function and can thus besampled with a high-resolution low-speed ADC 440.

Referring now to FIG. 5A, this figure illustrates another exemplaryembodiment for an analog-to-digital converter (ADC) 235′ and SIU 220.Only the differences between FIG. 4 and FIG. 5A will be discussed below.According to this exemplary embodiment, the second optional latch 430that can be coupled to the low-pass filter 435 has been removed. Theremoval of this latch can change the region of the signal that is beinganalyzed. Specifically, referring back to FIG. 4, latching the output ofthe second comparator 425 focuses the CDF characterization to theportion of the signal synchronized with the system clock and decisionoutput. By removing the latch as illustrated in FIG. 5A, the statisticalcharacterization applies to the entire received signal and not just thatportion which is used for the decision output.

Referring now to FIG. 5B, this figure illustrates another alternativeand exemplary embodiment for a multilevel receiver according to thepresent invention. In this exemplary embodiment, a high-resolutionanalog-to-digital converter (ADC) 440′ can measure the voltage of thereceived multilevel signal. The digitized multilevel signal can then beprovided to a digital signal processor (DSP) 505. The DSP 505 cangenerate a CDF of the data in software using the digitized samples.Furthermore, the DSP 505 can incorporate the operation of the controller445 in the SIU 220 to determine the decision thresholds. Then, insteadof using the first comparators 405, decoder 410, and latch 420, the DSP505 can perform the equivalent operations in software to identify eachsymbol of the multilevel signal.

Referring now to FIG. 5C, this figure illustrates another alternativeand exemplary embodiment for a multilevel receiver according to thepresent invention. Only the differences between FIG. 5C and FIG. 4 willbe discussed. FIG. 5C differs from FIG. 4 in the contents of the EDC.For the embodiment of FIG. 5C, the event that the EDC detectscorresponds to the received signal being between v_(rv)−Δ and v_(rv)+Δ.Thus, for small values of Δ, the average of the EDC output correspondsto a pdf estimate. The embodiment in FIG. 5C consequently bypasses theestimation of the CDF and directly estimates the pdf in the analogcircuitry. The EDC in this exemplary embodiment comprises a pair ofsecond comparators 574, 576 coupled to an AND gate 578. The EDC furthercomprises a second latch 430. As in FIG. 5A, the optional latch may beremoved from FIG. 5C to pose another alternative embodiment (not shownor described herein).

Exemplary Cumulative Distribution Function of Simulated ReceivedMultilevel Signal

Referring now to FIG. 6A, this figure illustrates a graph 600 of anempirical cumulative distribution function (CDF) 605 for the receivedmultilevel signal sampled at the eye openings 370 of FIG. 3C. The CDF605 is generated by taking the received signal v_(in)(t) and comparingit (with second comparator 425) to a controlled reference voltage v_(rv)to produce a binary signal that indicates whether the sampled signal isless than the set reference voltage. This binary signal may then belatched (through second optional latch 430) so that only eye-openingstatistics are considered. The binary signal is then low-pass filtered(with filter 435) which corresponds to averaging in time. Thus, thelow-pass filtered signal conveys the fraction of time (i.e. probability)that the received signal is less than the reference voltage.

Generating this probability estimate over a range of reference voltagesproduces CDF 605 that can completely characterize the received signal.In particular, the estimated noise distribution (and hence thresholdselection method) is free from restrictive assumptions such asGaussianity and symmetry that, while commonly used, can be detrimentalin some circumstances when dealing with multilevel data. But it is notedthat the present invention can also function when Gaussian and symmetryconditions hold.

Exemplary Probability Density Function (pdf) Derived from the CDF

Referring now to FIG. 6B, this figure illustrates a graph 610 of aprobability density function (pdf) 615 that can be derived from the CDF605 of FIG. 6A. The microcontroller 445 of the signal integrity unit 220can calculate this marginal pdf 615 as will be discussed below withrespect to the method illustrated in FIGS. 9-14. As is evident from pdf615, the noise incurred in transmission is signal dependent, e.g. themodes 620 of the pdf become shorter and wider as signal intensityincreases. For such situations involving signal dependent noise, optimaltransmission levels can be adapted to the noise in the channel tominimize the probability of error. This adaptation can be made by thetransmitter 110.

Referring now to both FIGS. 6A and 6B, the minimum number of requiredsample points of the pdf is 2N−1 where N is the number of symbols thatcan be transmitted. Specifically, at least 2N−1 reference voltages wouldbe required to describe the N peaks in the pdf (one peak for each of thecandidate symbols) and the N−1 troughs (one for each pair of adjacentsymbols). However, sufficiency of this minimal number of referencevoltages generally requires that (i) the true underlying pdf be composedof symmetric and signal independent noise distributions, (ii) thetransmission levels be uniformly spaced, and (iii) the estimationprocess be noise-free. None of these conditions are likely to besatisfied in practice, but their importance is vastly diminished as thenumber of reference voltages used is increased. In current practice, ADCtechnology is readily available to allow for high fidelity quantization(in excess of 14 bits or equivalently 4096 reference levels) for thesampling speeds required for the present invention.

Alternate Exemplary Embodiment for ADC and SIU of FIG. 7

Referring now to FIG. 7, another alternate exemplary embodiment for theADC 235″ and SIU 220″ is illustrated. Only the differences between FIG.4 and FIG. 7 will be discussed below. In this embodiment, the secondcomparator 425, latch 430, and low-pass filter 435 have been replacedwith a holding circuit 705.

In this exemplary embodiment, the CDF 605 and pdf 615 can be measured ina digital fashion (rather than the analog fashion described above) byusing a holding circuit 705. The holding circuit 705 can comprise atrack-and-hold circuit or a sample-and-hold circuit. The track-and-holdcircuit or the sample-and-hold circuit of holding circuit 705 can samplean input multilevel data signal and accumulate the samples over time.These samples can then be digitally processed to provide either amarginal pdf 605 or CDF 615. As before, the CDF 605 or marginal pdf 615may then be used by the microcontroller 445 to determine the optimaldecision threshold voltages for the comparators 405.

Additional Eye Diagram and Corresponding Digitally Processed Histogram

Referring now to FIGS. 8A and 8B, FIG. 8A illustrates a graph 800 oftime versus voltage depicting an exemplary “Eye”-diagram 805 for all4,096 received symbols corresponding to a transmitted signal that couldbe similar to the transmitted signal 305 of FIG. 3A. Eye diagram 805comprises the complete data set with all symbol periods overlaid on oneanother. Meanwhile, FIG. 8B illustrates a histogram 810 of measuredvoltages for the received analog multilevel signal that is sampled atrandom points in time. This histogram 810 is an example of a pdfestimate. This histogram 810 is comprised of a finite number of the mostrecent “n” samples taken by the holding circuit 705. As a new sample isdetermined, the oldest is removed from the sample set.

Ideally samples would occur at times centered temporally in thehigh-speed data stream's eyes. This would require critical timingrequirements and therefore not be expected to be cost effective.Instead, the voltage samples can be easily made at random times therebyallowing for the elimination of all critical timing circuitry. Theresult of random signal voltage sample times is similar to the idealsampling case due to the smaller probability of sampling during a signaltransition. While not dominant, samples do occur during a signaltransition which results in a data “floor” in the histogram, which canbe removed during subsequent signal processing.

Random sampling for this application means random to the high-speed datarate. This can be achieved by using a periodic sample rate, which is notharmonically related to the high-speed data rate. The actual averagesample rate of the random voltage samples is dictated by the thresholdupdate speed desired. If the communication channel is expected to varyquickly with time, the sample rate must be correspondingly high. As anexample, assuming that the channel varies with a 10 ms characteristictime and 1000 samples forms the histogram; average conversion speed onlyneed be 100,000 samples per second.

To produce the histogram 810 of FIG. 8B, the microcontroller 445 cansample the received analog voltage of the multilevel signal bytriggering the holding circuit 705 at some time random in relation tothe received data stream. The holding circuit 705 will necessarily havea capture bandwidth commensurate with the high-speed data stream, butwill only need to be able to sample at rate much lower than that of thehigh-speed data stream. The microcontroller 445 would then trigger thesecond ADC 440 conversion and record the resulting voltage. Themicrocontroller 445 can continue this process until adequate statisticinformation can be gathered to determine the appropriate decisionlevels.

Method For Decoding a Multilevel Signal

Referring now to FIG. 9, this figure is an exemplary logic flow diagramthat illustrates a method 900 for decoding a multilevel signal accordingto the embodiment illustrated by FIGS. 2 and 4. Differences inimplementation and operation compared to other embodiments are describedafter the full operation of the embodiment in FIGS. 2 and 4 isdiscussed. Certain steps in the processes described below must naturallyprecede others for the present invention to function as described.However, the present invention is not limited to the order of the stepsdescribed if such order or sequence does not alter the functionality ofthe present invention. That is, it is recognized that some steps may beperformed before, after, or in parallel with other steps withoutdeparting from the scope and spirit of the present invention.

The method 900 starts with step 905 in which a multilevel signal isreceived by the first comparator 405 of a multilevel receiver 150. Instep 907, the received multilevel signal is continuously sampled. Step907 basically describes an approach where the multilevel signal iscontinuously observed in order to decode the received data. In otherwords, step 907 may describe a loop where the multilevel signal iscontinuously sampled while the remaining steps of FIG. 9 are performedin parallel relative to the continuous sampling carried out in step 907.

Next in routine 910, a cumulative distribution function (CDF) based uponprevious symbols in the multilevel signal is calculated by themicrocontroller 445 of the signal integrity unit 220. Further details ofroutine 910 will be discussed below with respect to FIG. 10.

Next, in optional routine 915, a marginal probability density function(pdf) is calculated by the microcontroller 445 based upon the CDFcalculated in routine 910. As noted above, a marginal pdf can be definedas an “overall” pdf that results from random symbols being received. Amarginal pdf can comprise one or more conditional pdfs. A conditionalpdf is a pdf associated or corresponding to an individual symbol of amultilevel signal. Routine 915 is optional since decision thresholds canbe calculated from the CDF alone. Further details of routine 915 will bediscussed below with respect to FIGS. 11 and 12.

In routine 920, one or more decision thresholds based on at least one ofthe CDF and pdf can be determined. As mentioned previously, since thecalculation of the pdf is optional, decision thresholds can bedetermined from a calculated CDF alone. The microcontroller 445 isusually responsible for performing routine 920. Further details ofroutine 920 will be discussed below with respect to FIG. 13.

In step 925, the microcontroller 445 associates a threshold voltagelevel with each determined decision threshold calculated in routine 920.The microcontroller 445 forwards these voltage levels to the one or morefirst comparators 405 of the first analog-to-digital converter (ADC)235.

Next, in step 930, each first comparator 405 compares the receivedmultilevel signal with the one or more threshold voltages supplied bythe microcontroller 445. In step 935, the decoder 410 of the first ADC235 decodes the multilevel signal into one or more data streams basedupon the comparisons.

In routine 940, the microcontroller estimates the fidelity of thereceived multilevel signal. Further details of routine 940 will bediscussed below with respect to FIG. 14.

In step 945, the operation of the programmable analog signal processorslocated in the signal conditioning filter 215 can be adjusted by themicrocontroller 445 of the signal integrity unit 220 based upon thecalculated fidelity in routine 940. For example, the weightingcoefficients of a programmable delay line equalization filter could beadjusted to minimize the estimated probability of error inferred fromthis fidelity measure. Similarly, a controllable delay on the clocktiming may be adjusted to maximize the fidelity measure.

Next in step 950, the gain of the entire system can be adjusted based onthe range of received signal values inferred from the pdf as isdiscussed later.

Exemplary Embodiment of Sub-Method for Calculating CumulativeDistribution Function (CDF)

Referring now to FIG. 10, this figure illustrates exemplary steps forroutine 910 of FIG. 9 that calculates a CDF according to the exemplaryembodiment of the invention illustrated in FIG. 4. Routine 910 startswith step 1005 in which a reference voltage is swept over a range offeasible voltage levels by the microcontroller 445 of FIG. 4. Duringstep 1005, the second comparator 425 and low-pass filter 435 generate ananalog probability estimate v_(em) for a controlled reference voltagev_(rv). In other words, while sweeping v_(rv), v_(em) is measured. Themeasurement estimates the probability that the reference voltage exceedsthe received signal.

To understand why this occurs, consider the reference v_(rv) held at aconstant voltage. The output of the second comparator 425 is a binaryvalue equal to one if v_(in)≦v_(rv) and equal to 0 otherwise. Thisoutput can thus be written as the indicator function 1 (v_(in)≦v_(rv)).The low-pass filter 435 (labeled LPF) then averages this function overtime, i.e. it approximates the fraction of the time that v_(in) is lessthan v_(rv), or in other words, it approximates the probabilityP(v_(in)≦v_(rv)). More precisely, $\begin{matrix}\begin{matrix}{v_{em} = {v_{ol} + {K \cdot {{Avg}\quad\left\lbrack {1\left( {v_{i\quad n} \leq v_{rv}} \right)} \right\rbrack}}}} \\{\approx {v_{ol} + {K \cdot {\int_{- \infty}^{\infty}{1\left( {v_{i\quad n} \leq v_{rv}} \right){p\left( v_{i\quad n} \right)}{\mathbb{d}v_{i\quad n}}}}}}} \\{= {v_{ol}{\int_{- \infty}^{V_{rv}}{{p\left( v_{i\quad n} \right)}{\mathbb{d}v_{i\quad n}}}}}} \\{= {v_{ol} + {K \cdot {P\left( {v_{i\quad n} \leq v_{rv}} \right)}}}}\end{matrix} & (1)\end{matrix}$in which v_(ol) is the output voltage low state of the D-FF and K is aproportionality constant identical to the voltage swing from the D-FF(K=v_(oh)−v_(ol) where v_(oh) is the output voltage high).

Next in step 1010, the microcontroller 445 measures the resultingprobability estimate in order to generate the CDF 605 illustrated inFIG. 6A (which can be converted to a more intuitive pdf as discussedwith respect to FIG. 12 below). The sub-method then returns to routine915 of FIG. 9.

Exemplary Embodiment of Sub-Method for Calculating a Probability DensityFunction

Referring now to FIG. 12, this figure illustrates exemplary steps forroutine 915 of FIG. 9 that calculates a pdf according to the exemplaryembodiment of FIG. 4. Routine 915 starts with step 1205 in which a firstdifference is calculated for the CDF 605 determined in routine 910. Thefirst difference is generally the discrete time equivalent of aderivative. Specifically, for a sequence x[n], the first difference isthe sequence x[n]-x[n−1]. The result is the histogram h(v_(rv)) (notshown).

Unless a very large number of samples are used for each of the CDFpoints, there will be a considerable amount of statistical noise in theresulting pdf. Thus, step 1215 smoothes the histogram h(v_(rv)) (notshown) by filtering the histogram along the reference voltage.Specifically, h(v_(rv)) is convolved with a boxcar function to filterthe histogram along v_(rv) to produce the smoothed pdf g(v_(rv)). Thisoperation is motivated by regularity assumptions on the underlying noisedistribution. Furthermore, the application of the differentiation (step1205) and convolution to the CDF can be combined into one step, i.e.$\begin{matrix}{{g\left( \frac{v_{k} + v_{k + 1}}{2} \right)} = {\frac{1}{\left( {{2\quad R} + 1} \right)\Delta_{v}}\left\lbrack {{P\left( v_{k + R + 1} \right)} - {P\left( v_{k - R} \right)}} \right\rbrack}} & (2)\end{matrix}$where P(v_(k)) represents the CDF measured at voltage v_(k), R is the“radius” of the boxcar kernel, and Δ_(v), is the spacing between voltagesamples. Note that the calculation in Eq. (2) is no more computationallyintensive than taking a first difference (step 1205).

In step 1220, the histogram g(v_(rv)) (not shown) can be smoothed alongthe time domain. Specifically, the histogram is smoothed along the timedomain because should the pdfs vary slowly with time (if at all), bysmoothing in time, more samples are being used (in an iterativeframework) to estimate the probabilities without having to acquire manysamples to generate each probability estimate. In essence, measurementsof v_(em) are being recycled to estimate the pdf. To be more precise,first consider the pdf evaluated for a particular voltage v, i.e.consider the pdf on a pointwise basis. For each iteration n, a pdf valueg_(n)(v) (i.e. the pdf smoothed along voltage) is measured providing anoisy measurement of the true pdf value p_(n)(v) at time n, i.e. theobservation model isg _(n)(v)=p _(n)(v)+w _(n)(v)  (3)where w_(n)(v) is sample noise which is assumed to be white, i.e. theinner product of w_(n)(v) with w_(m)(v) is a Dirac function. Theevolution of the true pdf is modeled by the independent increments (andthus Markov) processp _(n)(v)=p _(n−1)(v)+u _(n)(v)  (4)where u_(n)(V) is another white noise process independent of w_(n)(v).The optimal estimator for the system given by the state dynamics in Eqs.(3) and (4) is the recursive estimator $\begin{matrix}\begin{matrix}{{q_{n}(v)} = {{\alpha\left\lbrack {{g_{n}(v)} \cdot {q_{n - 1}(v)}} \right\rbrack} + {q_{n - 1}(v)}}} \\{= {{\left( {1 - \alpha} \right){q_{n - 1}(v)}} + {\alpha\quad{g_{n}(v)}}}}\end{matrix} & \begin{matrix}\left( {5\quad a} \right) \\\left( {5\quad b} \right)\end{matrix}\end{matrix}$where q_(n)(v) denotes the pdf estimate at iteration n. Eq. (5a) iswritten in the form of a trivial Kalman filter (with Kalman gain α). Eq.(5b) is the Kalman filter rewritten in a form which makes theexponential memory decay of the process more explicit.

The reader may wonder why using Eq. (5) is preferable to simply usingmore samples to generate each g_(n)(v). Although both approaches can beused to provide an estimate with high statistical significance, thebrute force method of simply using more samples requires an associatedlarger amount of time to acquire those samples. The state-space approachin Eq. (2.4) recycles information so that the time required to generateeach g_(n)(v) can be considerably reduced. Eqs. (2) and (5) provide asmoothed (in both voltage and time) pdf 615 from the CDF providedthrough v_(em). The smoothing (in either voltage or time) steps 1215 and1220 are optional and may not be required if adequate statisticalsignificance can be achieved in a reasonable amount of time. Aftergenerating and optionally smoothing the pdf 615, the process thenreturns to routine 920 of FIG. 9.

Exemplary Embodiment of Sub-Method for Calculating Decision Thresholds

Referring now to FIG. 13, this figure illustrates exemplary steps forroutine 920 of FIG. 9 that determines the one or more decisionthresholds according to an exemplary embodiment of the presentinvention. To motivate the proposed methodology, the underlying analysisis presented here. It starts with a model of the received N-levelsignal. For each transmitted signal level x=A_(n) (nε{0, . . . , N−1}),the received symbol y has an associated conditional pdf p(y|x=A_(n)).This conditional pdf is the pdf for the received symbol conditioned ontransmitting a particular level A_(n). When the transmitted level is notknown (as is the case in realistic settings), the pdf characterizing thereceived symbol is the marginal pdf $\begin{matrix}{{p(y)} = {\frac{1}{N}{\sum\limits_{n = 0}^{N - 1}{p\left( {{y\text{❘}x} = A_{n}} \right)}}}} & (6)\end{matrix}$where it is assumed that all the symbols are equally likely to have beentransmitted. To illustrate the structure of such a marginal pdf, FIG. 15illustrates the marginal pdf (as a measured histogram) for an 16-levelsignal transmitted through 25 km of fiber. There are N=16 clearlyidentifiable modes of the pdf associated with the N transmission levels.There will always be at least N such distinct modes in situations wheresignal detection is possible. This property will be exploited for theoperation of the SIU.

The manner in which the pdf's structure is exploited will be through theuse of what this detailed description refers to as “ε-supports”. Thesupport of a function f(x) is mathematically defined to be the set{x|f(x)>0}, i.e. where the function is strictly positive. This isgeneralized to define the ε-support of a pdf asS _(ε) ={y|p(y)>ε}  (7)i.e. the ε-support conveys the range of values of y that are likely tobe observed. Furthermore, if the received signal is of reasonablefidelity (i.e. if the received symbols can be correctly detected with alow probability of error), then the ε-supports for the each of thetransmitted symbols do not overlap. Thus, a unique ε-support isidentified with each conditional pdf, i.e.S _(n,ε) ={y|p(y|x=A _(n))>ε}  (8)that conveys the range of values of y that are likely to be observedwhen transmitting level A_(n).

In practice, the conditional pdf's are usually unknown. However, anestimate {circumflex over (p)}(y) of the marginal pdf can be obtainedfrom the low-pass filtered event-detector output. Because the modes ofthe pdf are well separated (as in FIG. 15), for links of reasonablequality, reliable estimates can be obtained of the conditionalε-supports by taking them as the N regions composing the marginalε-support S_(ε). Specifically, the following three steps can be taken toobtain estimates of S_(n,ε).

-   1. In step 1305, the observed pdf {circumflex over (p)}(y) is    normalized to have a peak value of 1, i.e. define $\begin{matrix}    {{\hat{q}(y)} = \frac{\hat{p}(y)}{\max\limits_{y}\left\{ {\hat{p}(y)} \right\}}} & (9)    \end{matrix}$-   2. Next, in step 1310, {circumflex over (q)}(y) is thresholded    against ε (which is normalized to the range 0<ε<1), i.e. estimate    S_(ε) as    {circumflex over (S)}_(ε) ={y|q(y)>ε}  (10)    where the resulting Ŝ_(ε) is a set of intervals or “regions”.-   3. In step 1315, if there are more than N connected intervals    composing Ŝ_(ε), then iteratively merge the two regions that are    “closest” together until only N regions remain, where the measure of    “closeness” is given by the function: $\begin{matrix}    {{d\left( {A,B} \right)} = {\min\limits_{{a \in A},{b \in B}}\quad{\frac{a - b}{\lambda_{A} + \lambda_{B}}}}} & (11)    \end{matrix}$-    for any two regions A,BεŜ_(ε) where λ_(A) and λ_(B) are the lengths    (i.e. Lebesgue measure) of A and B, respectively. By “merging”    regions A and B, it means to take the convex hull of their union    (i.e. if A=[a_(low), a_(high)], B=[b_(low), b_(high)], and    a_(high)<b_(low), then the merger is taken as [a_(low), b_(high)]).

Note that one skilled in the art will understand that a variety offunctions can be used in place of Eq. (11) and still yield the desiredresult. All that is required is that the chosen function conveys anotion of the distance between sets. It should also be noted that step1315 above has the additional benefit that if the data exhibits multipleeye-lids or multiple-rails for a single transmitted symbol, then themerging will associate the multiple eye-lids according to theirunderlying common transmitted symbol. Specifically, link characteristicssuch as nonlinearities and intersymbol interference result in signaldistortions that manifest themselves as multi-modal conditional pdf's(or equivalently multiple eye-lids when the data is viewed as aneye-diagram). The multiple modes result in extra, but closely spaced,regions in Ŝ_(ε). The merging in step 1315 combines these multiple modesaccording to the underlying transmitted symbol.

In step 1320, possible threshold candidates are determined based uponthe combined remaining regions of the ε-supports. Specifically, havingestimated N ε-supports (each associated with one of the possible signallevels A_(n)), the following describes how the thresholds are setbetween the regions. First, each of the conditional pdf's p(y|x=A_(n))are modeled as a Gaussian (more to be said about the Gaussian modelingand application to non-Gaussian noise at the end of this subsection). Inparticular, for each transmitted signal level x=A_(n)(nε{0, . . . ,N−1}), the received symbol y is modeled with the conditional pdfp(y|x=A _(n))=φ(y; μ _(n), σ_(n))  (12)where φ(y; μ_(n), σ_(n)) is the Gaussian pdf with mean μ_(n) andstandard deviation σ_(n), i.e. $\begin{matrix}{{\varphi\left( {{y;\mu_{n}},\sigma_{n}} \right)} = {\frac{1}{\sqrt{2\quad\pi}\sigma_{n}}{{\exp\left\lbrack \frac{- \left( {y - \mu_{n}} \right)^{2}}{2\quad\sigma_{n}^{2}} \right\rbrack}.}}} & (13)\end{matrix}$Because each conditional pdf is assumed to be Gaussian, it ischaracterized by the conditional mean μ_(n) and standard deviationσ_(n). These two parameters are unknown quantities which must beestimated from the received data. To do this, the observed marginal pdf{circumflex over (p)}(y) and the ε-supports Ŝ_(n, ε) are used.Specifically, step 1320 can comprise the following substeps:

-   1. Compute the empirical mean and standard deviation based on    {circumflex over (p)}(y) but restricted to the domain where y is in    Ŝ_(n,ε), i.e. $\begin{matrix}    {{\overset{\_}{\mu}}_{n} = \frac{\int_{{\hat{\delta}}_{n,g}}{y\quad{\hat{p}(y)}{\mathbb{d}y}}}{\int_{{\hat{\delta}}_{n,g}}{{\hat{p}(y)}{\mathbb{d}y}}}} & (14) \\    {\overset{\_}{\sigma} = \sqrt{\frac{\int_{{\hat{\delta}}_{n,g}}{\left( {y - {\overset{\_}{\mu}}_{n}} \right)^{2}{\hat{p}(y)}{\mathbb{d}y}}}{\int_{{\hat{\delta}}_{n,g}}{{\hat{p}(y)}{\mathbb{d}y}}}}} & (15)    \end{matrix}$-   2. The quantities μ _(n) and σ _(n) correspond to the mean and    standard deviation of y conditioned on the events that (i) level    A_(n) was transmitted and (ii) the received value y lies in the set    Ŝ_(n,ε). However, the parameters μ_(n) and σ_(n) that are desired    are the mean and standard deviation conditioned only on the event    that level A_(n) was transmitted (i.e. the range of y is not    restricted). To obtain this quantity, μ _(n) and σ _(n) are scaled    appropriately with the set Ŝ_(n,ε) to unbias the estimates. Using    the appropriate normalization, this produces potential estimates of    μ_(n) and ρ_(n) as $\begin{matrix}    {{\hat{\mu}}_{n} = {\overset{\_}{\mu}}_{n}} & (16) \\    {{\hat{\sigma}}_{n}^{2} = \frac{{\overset{\_}{\sigma}}_{n}^{2}}{1 - \frac{2\quad ɛ\sqrt{\ln\quad\left( {1/ɛ} \right)}}{\sqrt{\pi}{{erf}\left( \sqrt{\ln\left( {1/ɛ} \right)} \right)}}}} & (17)    \end{matrix}$    where Eq. (16) implies that μ _(n) is already appropriately    normalized. However, the estimate given by Eq. (17) is not used as    it is written for the following reason. Even though ε is a    user-specified parameter, its use in Eq. (17) is not quite correct.    Specifically, recall that the threshold ε is applied to the marginal    pdf in contrast to the conditional pdf for level A_(n). Because the    true standard deviation σ_(n) will likely vary among the different    levels, the specified ε is correctly normalized only for the    conditional pdf with the largest peak (i.e. smallest σ_(n)) and the    use of this value of ε for all n, is inappropriate. To correct for    this level dependent fluctuation in ε, the value of ε is estimated    for each level A_(n) from the empirical probability measure of the    associated ε-support region. One skilled in the art can calculate    this revised value of ε as    ε_(n)=exp[−erfinv(N∫ _(S) _(n,ε) {circumflex over    (p)}(y)dy)²].  (18)-    Thus, in computing {circumflex over (σ)}_(n), ε_(n) is used as    defined by Eq. (18) instead of the user-specified ε.    These steps provide {circumflex over (μ)}_(n) and {circumflex over    (σ)}_(n) for all n, and thus, a characterization of all the    conditional pdf's.

FIGS. 16-17 (for a 16-level signal) show the results of this procedureon the data in FIG. 15. The measured pdf is shown in the solid curve.The difference between the measured pdf and the Gaussian mixture model(i.e. the modeling error) is shown with the dotted curve. FIG. 16 showsthe modeling error for the Gaussian model when the parameter estimatesare given by Eqs. (16) and (17) without the correction for ε; FIG. 17shows the error when the parameter estimates include the εcorrection in(18). The improvement from using ε_(n) is negligible for larger valuesof v_(in) (since ε is already approximately correct), but theimprovement is significant for smaller value of v_(in) where there arelarge differences among the σ_(n), and hence ε.

FIGS. 18-19 show the log-likelihood ratio (LLR) of the measured pdf tothe modeled pdf. The information content is the same as that in FIGS. 16and 17, but because the LLR is used in place of the difference, the plotemphasizes the goodness of fit in the tails of the distribution. FromFIGS. 18-19, it is seen that the Gaussian model does provide an accuratefit in the tails of the distribution down to the floor associated withthe limited amount of data.

Referring back to FIG. 13, as an alternative approach to estimatingμ_(n) and σ_(n), instead of using an approach based on the empiricalstatistics in Eqs. (14) through (17), the parameters can be estimateddirectly from the location and length of the ε-support Ŝ_(n,ε).Specifically, denoting Ŝ_(n,ε) as the closed interval [a, b], theconditional mean can be taken as{circumflex over (μ)}_(n)=(a+b)/2  (19)and the conditional standard deviation as $\begin{matrix}{{\hat{\sigma}}_{n} = \frac{b - a}{2\sqrt{2\quad{\ln\left( {1/ɛ} \right)}}}} & (20)\end{matrix}$As with Eq. (17), the estimate in Eq. (20) can be improved by usingε_(n) from Eq. (18) in place of ε.

Using the Gaussian model and estimated parameters {circumflex over(μ)}_(n) and {circumflex over (σ)}_(n) the decision thresholds can nowbe proposed. The nature of noise in communications channels is that thenoise perturbations are usually small rather than large. Not only isthis the case for the Gaussian noise model, but for many other noisemodels as well. For this reason, in this and the following section, weconsider only symbol errors associated with an adjacent level. Thesetypes of errors dominate the link performance characterization. Thus, itis sufficient to consider each pair of adjacent transmissions in aconventional on-off keying (OOK) context. In particular, the optimalthreshold to differentiate levels A_(n) and A_(n+1) is well approximatedby$\begin{matrix}{T_{n,{n + 1}} = \frac{{{\hat{\mu}}_{n}{\hat{\sigma}}_{n + 1}} + {{\hat{\mu}}_{n + 1}{\hat{\sigma}}_{n}}}{{\hat{\sigma}}_{n} + {\hat{\sigma}}_{n + 1}}} & (21)\end{matrix}$which has an associated probability of error of

-   -   Pr(error between symbols n and n+1|x=A_(n)) $\begin{matrix}        \begin{matrix}        {= {\Pr\quad\left( {{{{error}\quad{between}\quad{symbols}\quad n\quad{and}\quad n} + {1\text{❘}x}} = A_{n + 1}} \right)}} \\        {= {\frac{1}{2}{{erfc}\left( \frac{Q_{n,{n + 1}}}{\sqrt{2}} \right)}}}        \end{matrix} & (22)        \end{matrix}$        where Q_(n,n+1) is the traditional Q-factor estimate        $\begin{matrix}        {Q_{n,{n + 1}} = {\frac{{\hat{\mu}}_{n + 1} - {\hat{\mu}}_{n}}{{\hat{\sigma}}_{n} + {\hat{\sigma}}_{n + 1}}.}} & (23)        \end{matrix}$

The statistical analysis of routine 920 will usually be continuallyperformed; thereby adjusting the decision levels in real time tocompensate for time varying distortion/noise of the received signal.After routine 1320, the process for the current iteration returns tostep 925 of FIG. 9.

Prior to moving onto the next subsection, the robustness of the Gaussianmodel is discussed. Like much of the conventional art, the conditionalpdfs are modeled as Gaussian. However, because of the use of theε-supports to estimate the parameters of the Gaussian pdfs, the methodstill performs well in situations where the data is not Gaussiandistributed. Specifically, recall that the first step of the analysis isto compute N ε-support regions to characterize the region of significantprobability for the conditional pdfs. Thus, if the s-supports arecorrectly associated with the conditional pdfs, then the thresholds willbe established in the tails of the pdfs thus producing a low-probabilityof error. Fortunately, the method proposed in Eqs. (9)-(11), and thesurrounding text, should easily and correctly determine the ε-supportsbecause the modes of the pdfs will be well separated in realisticcommunications systems. Thus, even though a Gaussian model is used toestablish the thresholds in this sub-section, the use of the ε-supportsto determine the parameters still allow for non-Gaussian distributions(such as multi-modal distributions) to be handled as well.

Exemplary Embodiment of Sub-Method for Estimating Link Fidelity

Referring now to FIG. 14, this figure illustrates exemplary steps forroutine 940 of FIG. 9 that estimates the fidelity of a multilevel signalaccording to an exemplary embodiment of the present invention. Routine940 starts with step 1405 in which a conditional probability densityfunction (pdf) is estimated for each symbol of the multilevel signal.Next, in step 1410, the probability of error for the entire system canbe calculated. Specifically, the “wellness” of the data may be output asa voltage v_(fid) that conveys signal fidelity to analog signalconditioning circuits to provide an improved eye opening for reducederror rate.

This sub-method allows for error performance to be gauged withoutexplicit data error tests that can only be performed in artificialsettings where the transmitted values are known. Specifically, using theabove statistical characterization of the received data, the performanceof the link can be estimated using random data. Efforts in theconventional art usually estimate the error rate of the link bytransmitting a testing sequence of data (already known to the receiver)which is detected by the receiver. The receiver of the conventional artthen counts how many decoding errors were encountered.

The proposed method, in contrast, leverages the probabilistic modelingof the system to estimate link error rates without the transmission of apredetermined testing sequence. In particular, the error rate can beestimated while receiving random data during real-world operation byexploiting Eq. (22). Specifically, the overall link symbol error ratecan be obtained by averaging the probability of symbol error conditionedon a given transmitted symbol yielding: $\begin{matrix}\begin{matrix}{{\Pr\quad({error})} = {\frac{1}{N}{\sum\limits_{n = 0}^{N - 1}{\Pr\quad\left( {{error}\text{❘}A_{n}} \right)}}}} \\{= {\frac{1}{N}\begin{bmatrix}{{\Pr\quad\left( {{error}\text{❘}A_{0}} \right)} + {\Pr\quad\left( {{error}\text{❘}A_{N - 1}} \right)} +} \\{\sum\limits_{n = 1}^{N - 2}{\Pr\quad\left( {{error}\text{❘}A_{n}} \right)}}\end{bmatrix}}} \\{= {\frac{1}{2\quad N}\begin{Bmatrix}{{{erfc}\left( \frac{Q_{0,1}}{\sqrt{2}} \right)} + {{erfc}\left( \frac{Q_{{N - 2},{N - 1}}}{\sqrt{2}} \right)} +} \\{\sum\limits_{n = 1}^{N - 2}\left\lbrack {{{erfc}\left( \frac{Q_{{n - 1},n}}{\sqrt{2}} \right)} + {{erfc}\left( \frac{Q_{n,{n + 1}}}{\sqrt{2}} \right)}} \right\rbrack}\end{Bmatrix}}} \\{= {\frac{1}{N}{\sum\limits_{i = 0}^{N - 2}{{erfc}\left( \frac{Q_{n,{n + 1}}}{\sqrt{2}} \right)}}}}\end{matrix} & (24)\end{matrix}$Eq. (24) provides the symbol error probability. If desired, one canconvert this to a bit error probability. Specifically, if a Gray-codingscheme is used for the binary representation of the data, then eachsymbol error between adjacent levels produces a single bit error.Considering that signals composed of N levels require to log₂N bits fortheir binary representation, this yields a bit error probability of$\begin{matrix}\begin{matrix}{{P\quad\left( {{bit}\quad{error}} \right)} = \frac{P\quad\left( {{symbol}\quad{error}} \right)}{\log_{2}N}} \\{= {\frac{1}{N\quad\log_{2}N}{\sum\limits_{i = 0}^{N - 2}{{{erfc}\left( \frac{Q_{n,{n + 1}}}{\sqrt{2}} \right)}.}}}}\end{matrix} & (25)\end{matrix}$This bit error probability can then be converted into an “effective”Q-factor (i.e. the Q value of an OOK system that has the same bit errorrate as the multi-level system) via $\begin{matrix}\begin{matrix}{Q_{eff} = {\sqrt{2}{erfc}\quad{{inv}\left( {2\quad\Pr\quad\left( {{bit}\quad{error}} \right)} \right)}}} \\{= {\sqrt{2}{erfc}\quad{{{inv}\left( {\frac{2}{N\quad\log_{2}N}{\sum\limits_{n = 0}^{N - 2}{{erfc}\left( {Q_{n,{n + 1}}/\sqrt{2}} \right)}}} \right)}.}}}\end{matrix} & (26)\end{matrix}$The reliability measures in Eqs. (24)-(26) are all equivalent, and thus,any of these three can serve as a fidelity measure of the channelreliability. However, the effective Q-factor of Eq. (26) is morepractical for implementation because it is less susceptible to circuitnoise. Specifically, the error rate of the link is expected to be nearzero, and if either the bit or symbol error probability were used as thefidelity measure, then a small amount of noise in the circuitry woulddrown out the fidelity measure signal. The process then returns to step945 of FIG. 9.

Referring now to FIG. 20, this figure illustrates the measured pdf forN=16 level data received through 25 km of fiber. The line 2400 slicingthrough the pdf in FIG. 20 denotes the value of ε used to determine theε-supports (i.e. the regions where the pdf exceeds ε). Thresholds(obtained from Eq. (21)) are shown as vertical dashed lines with theassociated Q-factor (from Eq. (22)) for each pair of adjacent levels.The effective Q-factor (from Eq. (26)) for the multi-level system is3.1.

The validity of Eqs (22)-(26) is strongly dependent on the Gaussianmodel. If the noise is not Gaussian, then the Q-factor does not give theprobability of error as stated. However, in the non-Gaussian case, themethod still supplies an intuitive quantification of the fidelity of thereceived signal which is related to the probability of decoding error.Thus, while the numerical value provided by the fidelity measure may notexactly relate to detection error probability, it still characterizesthe fidelity of the link, i.e. large numerical values indicate bettersignal fidelity.

Exemplary Embodiment of Sub-Method for Gain Control

Referring back to step 950, because the ε-support regions calculated inroutine 920 represent all the voltage ranges where a candidate symbol islikely to be received, the ε-supports can be used to determine anappropriate gain normalization factor for the received signal. Inparticular, the largest and smallest voltages among all of the ε-supportregions represents the largest and smallest voltage likely to bereceived for a symbol transmission. These extreme values can thus beused to provide appropriate gain to scale the received signal such thatthe entire voltage swing of the system is utilized.

Specifically, the automatic gain voltage V_(agc) can be taken as thereciprocal of the size of the convex hull of all of the ε-supportregions, i.e. $\begin{matrix}{V_{agc} = \frac{1}{{\max\limits_{A}\quad\left\{ {\max\limits_{a \in A}\left\{ a \right\}} \right\}} - {\min\limits_{A}\quad\left\{ {\min\limits_{a \in A}\left\{ a \right\}} \right\}}}} & (27)\end{matrix}$where A represents the various ε-supports associated with each level,and thus the denominator represents the peak-to-peak voltage of thereceived signal.Alternative Exemplary Embodiment of Method for Decoding MultilevelSignals of FIG. 5A

Having given a detailed description of the embodiment illustrated byFIGS. 2 and 4, the embodiment given by the use of FIG. 5A in place ofFIG. 4 is now discussed. The operation and implementation of thisembodiment follows exactly as for FIG. 4 except that the second latch430 is removed. Thus the statistical characterization upon which all theanalysis is based covers the entire time span of the signal and not justthe portion synchronized with the first plurality of comparators 405.

Alternative Exemplary Embodiment of Method for Decoding MultilevelSignals of FIG. 5B

The embodiment given by the use of FIG. 5B in place of FIG. 4 is nowdiscussed. This embodiment differs from that illustrated in FIG. 4 inthe following manner. First, step 910 is omitted as the alternativeembodiment directly can calculate the pdf. This is done by sampling thesignal with the ADC 440′ which passes the samples onto the DSP. ADC 440′samples at the symbol rate with a high resolution. These samples areused both to decode the received symbol and produce the statisticalcharacterization in the DSP. The DSP collects the data samples and candigitally generate the pdf estimate. The remaining steps 920-950 canalso be absorbed into the DSP thereby obviating the need for thecontroller 445 in the SIU 220.

Alternative Exemplary Embodiment of Method for Decoding MultilevelSignals of FIG. 5C

The embodiment given by the use of FIG. 5C in place of FIG. 4 is nowdiscussed. The operation and implementation of this embodiment isidentical to that for FIG. 4 except that the filtered ED output v_(em)produces an estimate of the marginal pdf rather than the CDF. To see whythis occurs, note that the only difference between FIGS. 4 and 5C are inthe EDC. For FIG. 5C, the pair of second comparators 574, 576 produce asoutputs the indicator functions 1(v_(rv)−Δ<v_(in)) and1(v_(in)<v_(rv)+Δ). Thus, the quantity going into the low-pass filter435 is the binary function 1(v_(rv)−Δ<v_(in)<v_(rv)+Δ). Averaging thisfunction over time produces the probability estimateP(v_(rv)−Δ<v_(in)<v_(rv)+Δ) which is approximately proportional to thepdf p(v_(in)) for small values of Δ. Thus, step 910 is omitted for thisembodiment and the embodiment is the same as that for FIG. 4 in allother respects.

Alternative Exemplary Embodiment of Method for Decoding MultilevelSignals of FIGS. 7 and 11

Referring now to FIG. 11, this figure illustrates exemplary steps forroutine 915 of FIG. 9 that calculates a pdf according to the alternateexemplary embodiment associated with FIG. 7. The steps of routine 915correspond with the action taken by the ADC 235″ and track-and-hold 705illustrated in FIG. 7. It is noted that step 910 of FIG. 9 for theexemplary embodiment of FIG. 7 may be omitted.

Routine 915 starts with step 1105 in which the holding circuit 705 incombination with the ADC 220″ measure the voltage of the receivedmultilevel signal. Specifically, microcontroller 445 can sample thereceived analog voltage of the multilevel signal by triggering theholding circuit 705 at some time random in relation to the received datastream. The holding circuit 705 will necessarily have a capturebandwidth commensurate with the high-speed data stream, but will onlyneed to be able to sample at rate much lower than that of the high-speeddata stream.

Next in step 1110, the microcontroller 445 would then trigger the secondADC 440 conversion and record the resulting voltage. In step 1115, themicrocontroller 445 can collect the digitized measurements of thevoltages and obtain the histogram 810 of measured voltages asillustrated in FIG. 8B. Histogram 810 is an instance of a pdf estimate.The microcontroller 445 can continue this process until adequatestatistic information can be gathered to determine the appropriatedecision levels. The process then returns to routine 915 of FIG. 9.

CONCLUSION

The present invention uses a robust approach to setting the decisionthresholds that assumes neither unimodality nor symmetry of the noisedistributions but can also operate even if these assumptions hold. Theinvention exploits the estimated pdf and localized nature of the noiseto detect regions of significant probability. Each of these regionsshould correspond to where a candidate symbol i should be declared inthe decision process, i.e. each region determines the support of theconditional pdfs composing the observed marginal pdf. In cases where thenumber of regions exceeds the number of symbols (as may occur due tomulti-modal noise distributions and estimation errors), the inventionsystematically merges regions based on prior knowledge that (i)redundant eyelids are spaced very close together (relative to thespacing between eye-lids associated with differing symbols) and (ii) thenumber of candidate symbols is a known system parameter.

Further, the voltage decision thresholds produced by the algorithm areused by the fifteen high-speed comparators, which are followed bycombinational logic to properly decode the levels back to the encodeddata streams. The fifteen comparators and combinational logic areclosely related to a traditional flash ADC with the exception of optimalthreshold control (as per present invention) and decoding methods moreamenable to communication systems other than binary. The receiver 150converts the 16-level input into properly decoded data streams.

As noted previously, it should be obvious to one skilled in the art thatthe simple circuits illustrated in FIGS. 4, 5, and 7 can be expanded toN-level transmissions by incorporating N−1 high-speed comparators,adapting the decoding logic, and a higher resolution low-speed ADC forstatistic signal sampling.

One skilled in the art can appreciate that the methods described herecan be applied to other modulation schemes other than N-PAM. Examples ofsuch modulation schemes are phase shift keying, frequency shift keying,and combinations methods such as quadrature amplitude modulation. Theextension of the proposed method simply involves the appropriate changeof the control variable in the CDF/pdf estimation. Because norestrictive form the noise distribution is assumed, the presentinvention will adapt to the different data distribution associated withother modulation schemes, which the conventional art cannot.

While it is contemplated that the present invention is very suitable foroptical networking environments, it can be appreciated that the presentinvention could be easily employed in fields involving lower-speedcommunications. For example, lower-speed communication fields caninclude, but are not limited to, wireless applications, and applicationsutilizing modems such as telephone, digital subscriber lines (DSL), andanalog or digital cable.

It should be understood that the foregoing relates only to illustratethe embodiments of the present invention, and that numerous changes maybe made therein without departing from the scope and spirit of theinvention as defined by the following claims.

1-70. (canceled)
 71. A desymbolizer for receiving and decoding amultilevel communication signal, comprising: an analog-to-digitalconverter for receiving and decoding the multilevel communication signaland comprising one or more comparators; a signal integrity unit coupledto the analog-to-digital converter, comprising a microcontroller forcontrolling a threshold voltage of each comparator located in the firstanalog-to-digital controller, the microcontroller calculating at leastone of a cumulative distribution function and a probability densityfunction derived from the multilevel signal and associated with thethreshold voltage of each comparator.
 72. The desymbolizer of claim 71,wherein the analog-to-digital converter is a first analog-digitalconverter, and the signal integrity unit further comprises a secondanalog-to-digital converter coupled to the first analog-to-digitalcontroller
 73. The desymbolizer of claim 71, wherein the signalintegrity unit further comprises a digital-to-analog controller coupledto inputs of respective comparators located in the analog-to-digitalconverter.
 74. The desymbolizer of claim 71, wherein theanalog-to-digital converter comprises: a plurality of comparators forreceiving the multilevel signal; and a decoder coupled to the outputs ofthe comparators.
 75. The desymbolizer of claim 71, wherein the output ofthe analog-to-digital converter is coupled to a low-pass filter and theoutput of the low-pass filter is coupled to the microcontroller.
 76. Thedesymbolizer of claim 71, wherein the analog-to-digital convertercomprises a holding circuit.
 77. The desymbolizer of claim 76, whereinthe holding circuit comprises one of a track-and-hold circuit and asample-and-hold circuit.
 78. A desymbolizer for receiving and decoding amultilevel communication signal, comprising: an analog-to-digitalconverter for receiving and decoding the multilevel communicationsignal; a signal integrity unit coupled to the analog-to-digitalconverter for calculating and controlling one or more threshold voltagessupplied to the analog-to-digital converter, for calculating at leastone of a cumulative distribution function and a probability densityfunction derived from the multilevel signal and associated with the oneor more threshold voltages; and a signal conditioning filter thatequalizes and optimally filters the multilevel communication signalprior to the analog-to-digital converter, where the signal integrityunit selects an operating point of the signal conditioning filter basedupon the determination of the fidelity of the multilevel signal.
 79. Thedesymbolizer of claim 78, wherein the signal conditioning filtercomprises progammable analog signal processing modules.
 80. Thedesymbolizer of claim 78, wherein the signal conditioning filtercomprises an equalizer.
 81. The desymbolizer of claim 78, where thesignal conditioning filter comprises at least one clock recoverycircuit.
 82. The desymbolizer of claim 78, wherein the analog-to-digitalconverter comprises: a plurality of comparators for receiving themultilevel signal; and a decoder coupled to the outputs of thecomparators.
 83. The desymbolizer of claim 78, wherein the output of theanalog-to-digital converter is coupled to a low-pass filter and theoutput of the low-pass filter is coupled to the signal integrity unit.84. The desymbolizer of claim 78, wherein the analog-to-digitalconverter comprises a holding circuit.
 85. The desymbolizer of claim 84,wherein the holding circuit comprises one of a track-and-hold circuitand a sample-and-hold circuit.
 86. The desymbolizer of claim 84, whereinthe holding circuit samples the multilevel signal at random intervals.87. The desymbolizer of claim 84, wherein the holding circuit samplesthe multilevel signal at a periodic sampling rate wherein the period isan integer multiple of the symbol period.
 88. A method for determiningthreshold voltages of comparators in a multilevel signal receiversystem, comprising the steps of: evaluating voltage levels of amultilevel signal at predetermined time intervals; estimating aprobability density function based on the voltage levels; determiningone or more statistical centers positioned on local minima that arepresent in the probability density function; and adjusting one or morethreshold voltage levels based on the one or more statistical centers.89. The method of claim 88, further comprising the step of estimating acumulative distribution function based on a received multilevel signal.90. The method of claim 88, wherein evaluating voltage levels of amultilevel signal at predetermined time intervals comprises evaluatingvoltage levels at random time intervals.